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DOE OSTI2018

Expectation-maximization algorithm for amplitude estimation of saturated optical transient signals

This paper addresses parameter estimation for an optical transient signal when the received data has been right-censored. We develop an expectation-maximization (EM) algorithm to estimate the amplitude of a Poisson intensity with a known shape in the presence of additive background counts, where the measurements are subject to saturation effects. We then compare the results of our algorithm with those of an EM algorithm that is unaware of the censoring.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

National Smart Manufacturing Strategic Plan: To Facilitate More Rapid Development, Deployment and Adoption of Smart Manufacturing Technologies

Smart manufacturing technologies provide real-time data and insight to improve the productivity, efficiency, and competitiveness of U.S. manufacturing, creating the potential for new jobs in the manufacturing sector. These technologies can support U.S. manufacturers’ ability to increase throughput and energy efficiency, and decrease waste, defects, and costs. A wide range of manufacturing and industrial subsectors, particularly energy-intensive and energy-dependent industries, have the potential to benefit from smart manufacturing technologies. There are technical improvements still needed to reduce the costs and barriers (trained workforce and upskilling, software-hardware integration, cost, and technical barriers to deployment of advanced sensors, computing, and communication technologies for existing manufacturing assets) to the adoption of smart manufacturing technologies, especially to small and medium-sized manufacturers, and subsequently, increase the overall adoption rate of smart manufacturing technologies. This report outlines the Department of Energy’s (DOE) strategic plan to accelerate the development and implementation of smart manufacturing technologies in the United States and the actions DOE has taken to use these technologies in smart manufacturing for the United States. DOE’s plan to facilitate more rapid development, deployment and widespread adoption of smart manufacturing technologies derive from the 2018 Strategy for American Leadership in Advanced Manufacturing. The strategy outlines a vision for America’s leadership in advanced manufacturing including the development of intelligent manufacturing systems to optimize manufacturing facilities and support the manufacturing of transformative materials. DOE’s Clean Energy Smart Manufacturing Innovation Institute (CESMII), a Manufacturing USA Institute, focuses on accelerating the development and adoption of advanced sensors, controls, platforms, and models needed for smart manufacturing. The objective is to enhance U.S. manufacturing productivity and global competitiveness through the research and development of these technologies. Smart manufacturing has the potential to improve the overall performance, energy productivity, and efficiency of manufacturing, fostering the economic competitiveness of the manufacturing sector.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2019

A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns

A new approach is proposed for the indexing of electron back-scattered diffraction (EBSD) patterns. The algorithm employs a spherical master EBSD pattern and computes its cross-correlation with a back-projected experimental pattern using the spherical harmonic transform (SHT). This approach is significantly faster than the recent dictionary indexing algorithm, but shares the latter’s robustness against noise. The underlying theory is presented, followed by example applications, one on a series of Ni EBSD data sets recorded with decreasing signal-to-noise ratio, the other on a large shot-peened Al data set. The dependence of indexing speed and memory usage on the SHT bandwidth is explored. The speed gains of the new algorithm are achieved by executing real-valued Fast Fourier Transforms, explicitly incorporating crystallographic symmetry in the cross-correlation computation, and using efficient loop ordering to improve the caching behavior. The algorithm produces a cross-correlation array in the zyz Euler space; an orientation refinement procedure is proposed based on analytical derivatives of the Wigner d functions. As a result, the new approach can be applied to any diffraction modality for which the scattered intensity can be represented on a spherical surface.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Water at the graphene–substrate interface: interaction with short laser pulses

We have investigated the role of adsorption water in the local transformation of multilayer graphene deposited on an oxidised silicon substrate, which was exposed to nanosecond low-intensity focused laser radiation with a wavelength of 532 nm in the air. Experimental data obtained for a laser energy density E = 0.04 J cm{sup -2} suggest that the formation of micropits (craters) is a consequence of the multipulse removal of the layer of a water adsorbate, which is intercalated between graphene and the substrate, from the zone of laser irradiation of the graphene sheet. The energy threshold of graphene damage in the regions devoid of water was found to be higher in comparison with the initial one (0.058 against 0.048 J cm{sup -2}). According to computer simulations of the heating dynamics of the sample and the heat distribution in the substrate – adsorbate – graphene multilayer system, at energy densities corresponding to the experimental ones the water adsorbate layer heats to a temperature sufficiently high to form an increased-pressure vapour cavity under the graphene film. (interaction of laser radiation with matter)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

SU-F-J-94: Development of a Plug-in Based Image Analysis Tool for Integration Into Treatment Planning

Purpose: To extend the functionality of a commercial treatment planning system (TPS) to support (i) direct use of quantitative image-based metrics within treatment plan optimization and (ii) evaluation of dose-functional volume relationships to assist in functional image adaptive radiotherapy. Methods: A script was written that interfaces with a commercial TPS via an Application Programming Interface (API). The script executes a program that performs dose-functional volume analyses. Written in C#, the script reads the dose grid and correlates it with image data on a voxel-by-voxel basis through API extensions that can access registration transforms. A user interface was designed through WinForms to input parameters and display results. To test the performance of this program, image- and dose-based metrics computed from perfusion SPECT images aligned to the treatment planning CT were generated, validated, and compared. Results: The integration of image analysis information was successfully implemented as a plug-in to a commercial TPS. Perfusion SPECT images were used to validate the calculation and display of image-based metrics as well as dose-intensity metrics and histograms for defined structures on the treatment planning CT. Various biological dose correction models, custom image-based metrics, dose-intensity computations, and dose-intensity histograms were applied to analyze the image-dose profile. Conclusion: It is possible to add image analysis features to commercial TPSs through custom scripting applications. A tool was developed to enable the evaluation of image-intensity-based metrics in the context of functional targeting and avoidance. In addition to providing dose-intensity metrics and histograms that can be easily extracted from a plan database and correlated with outcomes, the system can also be extended to a plug-in optimization system, which can directly use the computed metrics for optimization of post-treatment tumor or normal tissue response models. Supported by NIH - P01 - CA059827.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: Part 1, data analysis and results

High-resolution broadband spectroscopy at near-infrared wavelengths (950 to 2450 nm) has been performed using externally dispersed interferometry (EDI) at the Hale telescope at Mt. Palomar. Observations of stars were performed with the “TEDI” interferometer mounted within the central hole of the 200-in. primary mirror in series with the comounted TripleSpec near-infrared echelle spectrograph. These are the first multidelay EDI demonstrations on starlight, as earlier measurements used a single delay or laboratory sources. We demonstrate very high (10×) resolution boost, from original 2700 to 27,000 with current set of delays (up to 3 cm), well beyond the classical limits enforced by the slit width and detector pixel Nyquist limit. Significantly, the EDI used with multiple delays rather than a single delay as used previously yields an order of magnitude or more improvement in the stability against native spectrograph point spread function (PSF) drifts along the dispersion direction. We observe a dramatic (20×) reduction in sensitivity to PSF shift using our standard processing. A recently realized method of further reducing the PSF shift sensitivity to zero is described theoretically and demonstrated in a simple simulation which produces a 350× times reduction. We demonstrate superb rejection of fixed pattern noise due to bad detector pixels—EDI only responds to changes in pixel intensity synchronous to applied dithering. This part 1 describes data analysis, results, and instrument noise. Lastly, a section on theoretical photon limited sensitivity is in a companion paper, part 2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Structure and behavior of water-laden CH 4 /air counterflow diffusion flames

A counterflow configuration was used to measure thermal and species structure in water-vapor diluted nonpremixed methane–air flames. The motivation is to understand the chemical and thermal effects that water has when it is introduced as a diluent into the fuel side. Here, this work is relevant to combustion processes where water is incorporated naturally in the fuel; e.g., methane hydrates, and when water is added intentionally for emission reduction such as in flares and H 2 O/fuel emulsions combustion. Experimental data are compared to 1-D computations. The agreement is generally very good, but the one dimensional counterflow diffusion model overpredicts flame temperature and major radical, OH, concentration very near extinction in highly diluted H 2 O–methane/air diffusion flames. Changes in flame position, flame width, and peak temperature with the addition of water were measured. Flame temperatures were measured with thin filament pyrometry. OH-PLIF is used to characterize the flame reaction zone with water dilution; the OH distribution, flame position and thickness from the OH-PLIF images were measured. The results show that the OH intensity and reaction zone thickness decreases with the increase in water. Predictions and experiments demonstrate that water mainly acts thermally to lower the flame temperature until extinction. The OH maximum intensity shifts towards the air side of the counterflow burner with water addition. OH is also measured with CO 2 dilution of the fuel stream, and the results are compared with H 2 O addition, including comparisons with the OH molar peak predictions obtained using the GRI 3.0 mechanism and the CHEMKIN Pro one dimensional counterflow model. The study indicates that water’s chemical effects are to change the production and depletion of OH, H and O radicals, especially near extinction. Chemical kinetics simulation of the flame demonstrates good agreement in OH and flame temperatures over a wide range of dilution away from extinction, particularly for CO 2 . Lastly, an over prediction of the water carrying capacity near extinction is found for highly water-diluted flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

An accelerated framework for predicting creep rupture lifetimes in engineering alloys

Confidently predicting high-temperature deformation, including creep and creep rupture, is paramount for the design and commercialization of candidate materials for advanced nuclear energy systems. To accelerate creep quantification, we introduce a framework that enables rapid, cost-effective, and reliable prediction of creep rupture lifetimes, minimizing reliance on time-intensive bulk creep testing. Unlike conventional creep analysis, which requires extensive time and resources, our method leverages a maximum of four short-term bulk creep tests as training data for prediction. This framework combines high-throughput nanoindentation up to 700 °C with these targeted bulk tests to inform our creep rupture model in order to predict rupture lifetimes. The strong agreement between our predictions and conventional experimental data demonstrates the effectiveness of our approach for accelerated creep analysis and lifetime prediction of structural components in high-temperature applications. Our multi-pronged approach motivates further integration of computational tools and advanced instrumentation to establish a universal framework for understanding high-temperature material responses.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns

Recently, there has been a growing interest in adapting serial microcrystallography (SMX) experiments to existing storage ring (SR) sources. For very small crystals, however, radiation damage occurs before sufficient numbers of photons are diffracted to determine the orientation of the crystal. The challenge is to merge data from a large number of such `sparse' frames in order to measure the full reciprocal space intensity. To simulate sparse frames, a dataset was collected from a large lysozyme crystal illuminated by a dim X-ray source. The crystal was continuously rotated about two orthogonal axes to sample a subset of the rotation space. With the EMC algorithm [expand–maximize–compress; Loh & Elser (2009). Phys. Rev. E , 80 , 026705], it is shown that the diffracted intensity of the crystal can still be reconstructed even without knowledge of the orientation of the crystal in any sparse frame. Moreover, parallel computation implementations were designed to considerably improve the time and memory scaling of the algorithm. The results show that EMC-based SMX experiments should be feasible at SR sources.

Chemistry↗

DOE OSTI2018

Development of a Virtual CFR Engine Model for Knocking Combustion Analysis

Knock is a major bottleneck to achieving higher thermal efficiency in spark ignition (SI) engines. The overall tendency to knock is highly dependent on fuel anti-knock quality as well as engine operating conditions. It is, therefore, critical to gain a better understanding of fuel-engine interactions in order to develop robust knock mitigation strategies. In the present work, a numerical model based on three-dimensional (3-D) computational fluid dynamics (CFD) was developed to capture knock in a Cooperative Fuel Research (CFR) engine. For combustion modeling, a hybrid approach incorporating the G-equation model to track turbulent flame propagation, and a homogeneous reactor multi-zone model to predict end-gas auto-ignition ahead of the flame front and post-flame oxidation in the burned zone, was employed. In addition, a hybrid methodology was implemented wherein a laminar flame speed lookup table generated a priori from a chemical kinetic mechanism could be used to provide flame speed as an input to the G-equation model, instead of using conventional empirical correlations. Multi-cycle Reynolds-averaged Navier-Stokes (RANS) simulations were performed for two different spark timings (STs) corresponding to non-knocking and knocking conditions, with other operating conditions kept the same as those of a standard research octane number (RON) test. Isooctane was considered as the fuel for the numerical study. Two different reduced kinetic mechanisms were employed to describe end-gas auto-ignition chemistry and to generate the flame speed lookup table. Experimental data, including intake/exhaust boundary conditions, was provided by an isooctane ST sweep study conducted in an in-house CFR engine. Moreover, cylinder wall/valve/port surface temperatures and residual gas fraction (RGF) were estimated using a well-calibrated one-dimensional (1-D) model. On the other hand, a novel methodology was also developed to analyze experimental data for the knocking case and identify the most representative cycle. For the non-knocking case, a good agreement was found between experiment and CFD simulation, with respect to cycle-averaged values of 10% burn point (CA10), 50% burn point (CA50), and peak pressure magnitude/location. The virtual CFR engine model was also demonstrated to be capable of predicting average knock characteristics for the knocking case, such as knock point, knock intensity, and energy of resonance, with good accuracy.

42 ENGINEERING↗

DOE OSTI2018

On the role of last closed drift shell dynamics in driving fast losses and Van Allen radiation belt extinction

We present observations of very fast radiation belt loss as resolved using high time resolution electron flux data from the constellation of Global Positioning System (GPS) satellites. The time scale of these losses is revealed to be as short as ~0.5–2 hr during intense magnetic storms, with some storms demonstrating almost total loss on these time scales and which we characterize as radiation belt extinction. The intense March 2013 and March 2015 storms both show such fast extinction, with a rapid recovery, while the September 2014 storm shows fast extinction but no recovery for around 2 weeks. By contrast, the moderate September 2012 storm which generated a three radiation belt morphology shows more gradual loss. Here, we compute the last closed drift shell (LCDS) for each of these four storms and show a very strong correspondence between the LCDS and the loss patterns of trapped electrons in each storm. Most significantly, the location of the LCDS closely mirrors the high time resolution losses observed in GPS flux. The fast losses occur on a time scale shorter than the Van Allen Probes orbital period, are explained by proximity to the LCDS, and progress inward, consistent with outward transport to the LCDS by fast ultralow frequency wave radial diffusion. Expressing the location of the LCDS in L*, and not model magnetopause standoff distance in units of RE, clearly reveals magnetopause shadowing as the cause of the fast loss observed by the GPS satellites.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Beam loss modeling and mitigation due to intra-beam stripping

Intra-Beam Stripping (IBS) is a critical beam loss mechanism in high-intensity H- linacs and presents a significant limitation to increasing beam power. This work presents a computational framework to evaluate and mitigate IBS-induced beam loss along the Spallation Neutron Source (SNS) LINAC. Our calculation is based on an analytic theory and involves evaluation of a 9D integral using the Monte-Carlo technique. We first benchmarked our calculations against simplified, analytically solvable cases. We then applied our algorithm to Gaussian bunches with a known probability density function (PDF). We next expanded our algorithm to arbitrary bunch distributions using the Neural Spline Flow (NSF) models trained on PyORBIT tracking data. In the future, we plan to validate our algorithm experimentally and apply it to design IBS mitigation strategies.

Nln, Shivam [ORNL]↗

DOE OSTI2020

Land Model Testbed: Accelerating Development, Benchmarking and Analysis of Land Surface Models

A Land Model Testbed (LMT), designed to provide a computational framework for systematically assessing model fidelity and supporting rapid development of complex multiscale models, offers a general-purpose workflow for conducting large ensemble simulations of multiple land surface models, post-processing large volumes of model output, and evaluating model results. It leverages existing tools for launching model simulations and the International Land Model Benchmarking (ILAMB) package for assessing model fidelity through comparison with best-available observational datasets. Increased complexity and proliferation of uncertain parameters in process representations in land surface models has driven the need for frequent and intensive testing and evaluating of models to quantify uncertainties and optimize parameters such that results are consistent with observations. The LMT described here meets these needs by providing tools to run thousands of ensemble simulations simultaneously and post-process their output files, by automating execution of an enhanced version of ILAMB with site-specific benchmarks and multivariate functional relationships, and by offering ensemble diagnostics and a customizable dashboard for displaying model performance metrics and associated graphics. We envision the LMT capabilities will serve as a foundational computational resource for a proposed user facility focused on terrestrial multiscale model--data integration.

Sreepathi, Sarat↗

DOE OSTI2018

Automation of Data Collection Methods for Online Monitoring of Nuclear Power Plants

Maintenance activities in the United States nuclear power industry are mainly centered on preventive and corrective maintenance. Predictive maintenance, which is a variable time basis maintenance strategy that is dependent on the condition of the equipment, is less utilized but potentially more effective. In the current maintenance practices, the nuclear power plants rely on manual processes to supply information to a human decision making process. The plants have several processes that generate information that is not typically used beyond the intended target for collecting that information. This information is a source of data that is manually collected by labor intensive tasks. The data is therefore expensive to collect, yet limited in use. The industry has realized the opportunity present in reducing the labor intensive tasks by automating them and increasing the uses of the data collected by either developing advanced predictive maintenance methods using data-driven decision making that could span from trending to machine learning and artificial intelligence. This shift in maintenance strategy may result in high cost saving impact. In addition to reducing labor requirements and frequency of maintenance activities, this shift in strategy will reduce the materials portion of the operations and maintenance cost as well. The aim of this specific effort is to focus on the automation of data collection process. It is part of a series of planned efforts to target multiple elements of migrating the current preventive maintenance approach in nuclear power plants to a data-driven approach. These elements include data collection, management, analysis, visualization, in addition to value analysis and change enabling. The other five elements of migration were not considered because they are planned to be explicitly studied in multiple parallel efforts. Challenges including regulations requirements or limitations are planned in a future effort that focuses on change enabling. The risk and benefit/cost of the approach shift is planned in another effort targeted towards value. The storage, communication, computational power, data architecture, and protection are part of the information infrastructure and are planned in dedicated data management effort. The best means to present the data for assisted human decision making is planned in a data visualization effort. The data interpretation and patterns recognition for machine decision making is planned through multiple efforts in data analytics over the following years. This work identified seventeen data sources collection methods in nuclear power plants that could be automated for an integrated data platform that enables comprehensive and informed decision making. For each of the identified seventeen data sources, the base, modern, and state of the art states were described. The current state of data collection used by most utilities was identified as the "base state". The current achievable state was identified as the "modern state", a state that has either been achieved by at least some US utilities or in other industries. The future state that requires research and development to reach was identified as the "state of the art" state. The described states used an out-of-the-box thinking approach. This effort found that there is a hug potential for task automation and data fidelity improvements by evolving the current industry data collection methods. The majority of the processes analyzed were found to be manual and labor intensive and fell in the base state. As a result, the modern state often targeted reducing the manual logging efforts by using electronic and semi-intelligent means or complementing the work with sensors and mobile or fixed technologies that can reduce the demand of labor activities. The state of the art state involved applications advanced methods of data correlation, data mining, and machine learning along with increasing the spatial distribution and fidelity of data, coupling multiple data sources, and enabling the use of sophisticated mobile devices and machine comprehension methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

A new framework to map fine resolution cropping intensity across the globe: Algorithm, validation, and implication

We report accurate estimation of cropping intensity (CI), an indicator of food production, is well aligned with the ongoing efforts to achieve sustainable development goals (SDGs) under diminishing natural resources. The advancement in satellite remote sensing provides unprecedented opportunities for capturing CI information in a spatially continuous manner. However, challenges remain due to the lack of generalizable algorithms for accurately and efficiently mapping global CI with a fine spatial resolution. In this study, we developed a 30-m planetary-scale CI mapping framework with the reconstructed time series of Normalized Difference Vegetation Index (NDVI) from multiple satellite images. Using a binary crop phenophase profile indicating growing and non-growing periods, we estimated pixel-by-pixel CI by enumerating the total number of valid cropping cycles during the study years. Based on the Google Earth Engine cloud computing platform, we implemented the framework to estimate CI during 2016–2018 in eight geographic regions across continents that are representative of global cropping system diversity. Comparison with PhenoCam network data in four cropland sites suggests that the proposed framework is capable of capturing the seasonal dynamics of cropping practices. Spatially, overall accuracies based on validation samples range from 80.0% to 98.9% across different regions worldwide. Regarding the CI classes, single cropping systems are associated with more robust and less biased estimations than multiple cropping systems. Finally, our CI estimates reveal high agreement with two widely used land surface phenology products, including Vegetation Index and Phenology V004 (VIP4) and Moderate Resolution Imaging Spectroradiometer Land Cover Dynamics (MCD12Q2), meanwhile providing much more spatial details. Due to its robustness, the developed CI framework can be potentially generalized to produce global fine resolution CI products for food security and other applications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

MemHC: An Optimized GPU Memory Management Framework for Accelerating Many-body Correlation

The many-body correlation function is a fundamental computation kernel in modern physics computing applications, e.g., Hadron Contractions in Lattice quantum chromodynamics (QCD). This kernel is both computation and memory intensive, involving a series of tensor contractions, and thus usually runs on accelerators like GPUs. Existing optimizations on many-body correlation mainly focus on individual tensor contractions (e.g., cuBLAS libraries and others). In contrast, this work discovers a new optimization dimension for many-body correlation by exploring the optimization opportunities among tensor contractions. More specifically, it targets general GPU architectures (both NVIDIA and AMD) and optimizes many-body correlation’s memory management by exploiting a set of memory allocation and communication redundancy elimination opportunities: first, GPU memory allocation redundancy: the intermediate output frequently occurs as input in the subsequent calculations; second, CPU-GPU communication redundancy: although all tensors are allocated on both CPU and GPU, many of them are used (and reused) on the GPU side only, and thus, many CPU/GPU communications (like that in existing Unified Memory designs) are unnecessary; third, GPU oversubscription: limited GPU memory size causes oversubscription issues, and existing memory management usually results in near-reuse data eviction, thus incurring extra CPU/GPU memory communications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Influence of intrinsic decoherence on tripartite entanglement and bipartite fidelity of polar molecules in pendular states

An array of ultracold polar molecules trapped in an external electric field is regarded as a promising carrier of quantum information. Under the action of this field, molecules are compelled to undergo pendular oscillations by the Stark effect. Particular attention has been paid to the influence of intrinsic decoherence on the model of linear polar molecular pendular states, thereby we evaluate the tripartite entanglement with negativity, as well as fidelity of bipartite quantum systems for input and output signals using electric dipole moments of polar molecules as qubits. According to this study, we consider three typical initial states for both systems, respectively, and investigate the temporal evolution with variable values of the external field intensity, the intrinsic decoherence factor, and the dipole-dipole interaction. Thus, we demonstrate the sound selection of these three main parameters to obtain the best entanglement degree and fidelity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Research software engineering: Professionalization, roles, and identity

This report summarizes the results of a study of research software professionals based on 17 interviews conducted at U.S. national laboratories and academic institutions. The study focuses on understanding the emerging professional role of research software engineer (RSE) and examining how the history of software engineering might be relevant to the emergence of research software engineering as a professional movement. The report first uses interview data to identify several models of professional identity for research software professionals. These include dominance models in which a person strongly identifies with a single professional identity (such as RSE), and multiplicity models in which an individual sees an identity like RSE as just one facet of their overall professional role. Next, it identifies three types of work situations for software professionals at national laboratories, covering those who work in dedicated RSE organizations, those who play an integral role in large multiphysics code projects, and those who work in a more isolated capacity to provide software development support for less computationally intensive research projects. It then reviews some key ideas from the sociology of professions in the context of the software engineering profession, suggesting parallels between the current RSE professional movement and aspects of the history of software engineering. It concludes by suggesting some potential practical implications of these findings for the RSE movement and professional organizations.

97 MATHEMATICS AND COMPUTING↗